Hi, I have the following dynamical system,

$\displaystyle x_{n+1}={x_n}^2-{y_n}^2+a$

$\displaystyle y_{n+1}=2x_ny_n$

Where a is real.

And I am asked to consider the set of points on a circle of radius r and centre origin and show that they are mapped to another circle under one iteration.

How do I go about this? I know the equation for the circle is of course $\displaystyle x^2+y^2 = r^2$. Can someone please give me a clue how to start?

Thanks,

Katy